Knowing this positioning error of the receiver makes it possible to determine a volume for which the probability of presence of the receiver is above a threshold set by a standard. Knowing this volume thus makes it possible, for example, to determine the minimum distance at which two aircraft must not come closer to each other. Knowing this information is in particular necessary for integrity services. The term integrity service refers to the capability of a system to supply an alert to the pilot when the navigation system can no longer be used with the requisite performance in terms of user risk.
These error determination systems may be used in aircraft but also in ground vehicles or ships, for example.
Systems are known in the prior art in which information representing the positions of the satellites, and times of passage through the ionosphere as well as information representing the error on these positions and these times of passage are sent to the various receivers. Knowing this information makes it possible to determine the position error of the receiver, also referred to as the integrity of the position of the object located by the receiver.
It is known in the prior art that the items of information representing errors are marginal standard deviations (σi) of the distributions of the errors committed. Thus the error distribution is modelled by a centred Gaussian law of the form N(0, σi2). However, the modelling of the error distribution in the form of a centred Gaussian law is too coarse, and leads to the need for a safety margin to be applied, which is in some cases too large. This is particularly the case when the combination of the marginal standard deviations (σi), of the position error of each satellite used, must be small to allow sufficient accuracy for the performance of the maneuvers to be executed. In such cases, the margin, chosen to cover the lack of fit of a model based on centred Gaussians, too frequently makes the service unavailable. It has also been possible to demonstrate that the use of centred Gaussians is only correct from a mathematical point of view if one can posit the hypothesis that the errors are distributed in a unimodal and symmetrical way, which is in no way guaranteed as a general rule.